Statistics, down to Earth

Course Outline
Our flagship course, taught over 4.5 days.

Describing Data
When to tuse a median vs a mean
Dealing with skewed, non-normal data
Dealing with outliers
When to transform the scale

Seven Urban Legends in Environmental Statistics
Do parametric methods have more power than nonparametric tests?
Why t-tests on logarithms don't test differences in means
Why t-tests don't test whether one group has higher values than the second
and more....

How Hypothesis Tests Work
Structure of hypothesis testing
Their jargon explained
Parametric, nonparametric and permutation tests. When to use each.
1-sided and 2-sided tests
Checking data distributions
Illustration: How tests obtain a p-value

Statistical Intervals
Confidence, prediction, tolerance intervals
Intervals with small sample sizes
Coping with skewed data
Bootstrap intervals — and why to use them instead of t-intervals
Exercise: the UCL95 and other intervals

Comparing Two Groups of Data
Are means, medians different?
Parametric, nonparametric and permutation tests
Testing paired data
Have standards been met?
The quantile test
Permutation tests — test the mean for non-normal distributions

(if there’s time) How many observations do I need?
Power and sample size
Which units to use?
Numbers of obs for parametric and non-parametric tests
Software available

Comparing Three or More Groups
One- and two-factor ANOVA
Nonparametric Kruskal-Wallis test
Multiple comparison tests: who’s different?
Permutation one-factor test: never worry about a normal distribution again!

Testing differences in Variability/Precision
Characterizing differences in variability
Levene’s & Fligner-Killeen tests
Why NOT to use Bartlett’s test

Linear and monotonic correlation
r, rho and tau
Permutation test for Pearson’s r correlation
The Theil-Sen line: a linear median

Linear Regression
Building a good regression model
Better measures of quality than r-squared
Hypothesis tests, confidence and prediction intervals
Consequences of transforming the Y variable
Bootstrapping tests for significance - an alternative to transformations

Multiple Regression
How to build a good multiple regression model
Why plots of Y vs each X don't work, and what to do instead
Model selection methods better than r-squared or stepwise
Bootstrapping tests for significance - an alternative to transformations

Analysis of Covariance
Testing whether there is one or more than one regression line
Are there differences in intercept and slope?
Modeling seasonal changes

Trend Analysis
Selecting a trend test
Regression vs. Mann-Kendall approaches
Monotonic vs. step trends
Dealing with seasonality: the Seasonal-Kendall test for trend
Detecting consistent regional trends across sites
R routines for trend testing


DAY 5 (half day)
Handling Nondetect Data Correctly
Why not substitute 1/2 the detection limit?
Simple methods without substitution
Introduction to survival analysis methods

Contingency Tables
Does the frequency change between groups?
Application to nondetect and other cateogories
Bootstrapping contingency tables

Logistic Regression
Regression for categorical responses
Effect of X variables on the odds
Modeling nondetects, qualitative methods, and the probability of something bad happening
Multicollinearity and hypothesis tests